Optical spintronics in organic-inorganic perovskite photovoltaics

Organic-inorganic halide ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ solar cells have attracted enormous attention in recent years due to their remarkable power conversion efficiency. When inversion symmetry is broken, these materials should exhibit interesting spin-dependent properties as well, owing to their strong spin-orbit coupling. In this work, we consider the spin-dependent optical response of ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$. We first use density functional theory to compute the ballistic spin current generated by absorption of unpolarized light. We then consider diffusive transport of photogenerated charge and spin for a thin ${\mathrm{CH}}_3{\mathrm{NH}}_3{\mathrm{PbI}}_3$ layer with a passivated surface and an Ohmic, nonselective contact. The spin density and spin current are evaluated by solving the drift-diffusion equations for a simplified three-dimensional Rashba model of the electronic structure of the valence and conduction bands. We provide analytic expressions for the photon flux required to induce measurable spin densities, and propose that these spin densities can provide useful information about the role of grain boundaries in the photovoltaic behavior of these materials. We also discuss the prospects for measuring the optically generated spin current with the inverse spin Hall effect.

Figure 1

(a) Comparison between Wannier interpolated (solid line) and quantum-espresso (dots) bands. (b) Zoom in of the conduction bands near the $\mathrm{\Gamma }$ point, along with fitting to the Rashba Hamiltonian. The fitting parameters are $m_c^{*}=0.11m_e, {\alpha }_c=-0.22\mathrm{eV}\mathrm{nm}$. For the valence band (not shown), the fitting parameters are: $m_v^{*}=0.14m_e, {\alpha }_v=0.15\mathrm{eV}\mathrm{nm}$. (c) Drawing of constant energy circles for $k_z=0$, showing the $\mathbf{k}$-dependent spin texture of the conduction bands. A current-carrying distribution results in more states occupied in the $k_x>0$ half of the plane (denoted by a thicker line), and a net spin accumulation in the $-y$ direction.

Figure 2

(a) The total spin current response versus photon energy (subtracted by the band gap energy $E_g$), along with the separate electron and hole contributions (b) the total spin current response for electron velocity in the $x$ direction, and light polarized in the $x$ direction. (c) the same as (b), but with light polarized in the $y$ direction. (d) the total spin current response for electron velocity in the $y$ direction, and light polarized in the $y$ direction.

Figure 3

(a) shows the system geometry. The gradient in shading of the sample indicates the length scale of generation electron-hole pair generation, ${\beta }^{-1}$. The blue arrow on the contact in the $z$ direction denotes the direction of symmetry breaking in the perovskite, and the direction of the current induced by the inverse spin Hall effect. (b) is the charge and spin density for $\beta L\ll 1, \tilde{\mu }=0$. Densities are scaled by ${\varphi }_0\beta {\tau }_n$. (c) shows the same for $\beta L=10$. (d) shows the charge and spin density for an unrealistically large value of $\tilde{\mu }$ (100 times larger than the expected value), as an illustration of the effect of a spatially varying ballistic spin current on the diffusion.

Figure 4

Depiction of system geometry used for the detection of spatially nonuniform charge diffusion due to the presence of grain boundaries (shown as dashed line). The perovskite absorber is taken to be $p$ type and sandwiched between selective contacts. An electrostatic potential attracts minority carriers (electrons) to the grain boundary core, where they diffuse to the electron collecting contact. In the schematic, the electron velocity is denoted with straight black arrows, and the resulting spin density is denoted with thick blue arrows. The detecting photons are used to measure the spin density on the $x-y$ plane with the magneto-optical Kerr effect, and the crystal symmetry breaking direction of the grains must both be in the $z$ direction. ${\varphi }_0$ represents the photon flux which excites electron-hole pairs in the absorber.